Help with ACT math prep

Question

The value of a used car can be modeled by the formula V=Vo(1-r)^t where Vo is the car's purchase price, in dollars; r is the car's constant annual rate of decrease in value, expressed as a decimal; and V is the car's dollar value at the end of t years.

1. Show the formula solved for r (I got this answer: r = 1 minus the "t root" of V/Vo)
2. A used car with a purchase price of $20,000 has a constant annual rate of decrease in value of 0.1 According to the model, what is the value of the car at the end of 3 years? (I got this answer: $14,580)
3. A used car has a constant annual rate of decrease in value of 0.075. According to the model, what expression would give the number of years after purchase for the car to reach a value that is 50% of its purchase price? (This one, I have no idea!)

Answer 1

You are lookin good on the first 2!

For the third one, just remember that V in this case is just (.5)V_o

So .5Vo = V_o(1-.075)^t or .5 = (.925)^t Then log(.5) = t(log(.925))

t = log(.5)/log(.925) = 8.89 years